Successful neutrino models have to show a mass and flavour structure in accordance with the latest oscillation data [1]}.
Many of these models realize such a pattern via imposed flavour symmetries which introduce symmetry protected zero modes in the neutrino mass matrix.
A commonly considered two-flavour symmetry leads to two-zero textures which can successfully explain neutrino oscillation data but predict \(\sum m_\nu \ge 0.12~\mathrm {eV}\)  in 5 out of 7 viable realizations [2]}.
Furthermore, even though other models may not strictly predict neutrino masses in conflict with the current cosmological bound many of them accommodate for \(\sum m_\nu \ge 0.12~\mathrm {eV}\)  across large regions of the parameter space.
We will focus on the case of a neutrino model with an underlying \(U(1)_{\mu -\tau }\)  flavour symmetry and incorporate an invisible neutrino decay via a simple extension of the seesaw framework.
